$y =\dfrac{2\sin x - 3\cos x -1}{\sin x + \cos x -4}$
$\to y\sin x + y\cos x - 4y = 2\sin x - 3\cos x -1$
$\to (y-2)\sin x + (y-3)\cos x = 4y -1$
Phương trình có nghiệm
$\Leftrightarrow (y -2)^2 + (y -3)^2 \geq (4y-1)^2$
$\Leftrightarrow 7y^2 + y - 6 \leq 0$
$\Leftrightarrow -1 \leq y \leq \dfrac{6}{7}$
$\Rightarrow \begin{cases}M = \dfrac{6}{7}\\m = -1\end{cases}$
$\Rightarrow M^2 + m^2 + Mm = \dfrac{36}{49} + 1 -\dfrac{6}{7}=\dfrac{43}{49}$
